In fact, there are multiple discrepancies between these two verses, what did really happen?

Matthew 27:5-8

5 And he cast down the pieces of silver in the temple, and departed, and went and hanged himself. 6 And the chief priests took the silver pieces, and said, It is not lawful for to put them into the treasury, because it is the price
of blood. 7 And they took counsel, and bought with them the potter's field, to bury strangers in. 8 Wherefore that field was called, The field of blood, unto this day.

Now compare that to what the book of Acts says about this:

Acts 1:18-19

18 Now this man purchased a field with the reward of iniquity; and falling headlong, he burst asunder in the midst, and all his bowels
gushed out. 19 And it was known unto all the dwellers at Jerusalem; insomuch as that field is called in their proper tongue, Aceldama, that is to
say, The field of blood.

If you read these two passages carefully you will notice that they seem to disagree on the following points (my paraphrase):

Matthew says Judas didn't use the money at all but rather threw it down the temple's floor (in fact, the priests used the money to buy a field), but Acts says that Judas himself bought a field with the money he 'earned' from his betrayal.

Matthew says that Judas died by hanging himself, but Acts says that Judas died by 'falling headlong' in the midst of the field he bought and 'burst asunder', spilling his guts out.

Matthew says that the field was called the 'field of blood' because it was bought with 'blood money', but Acts says that the field is called 'field of blood' because when Judas fell and died he spilled his guts and blood over the field.

These seem to be two completely different stories. How can these to different accounts be reconciled?

Another rendering of "hanged" is "strangled." Strangling was a common form of suicide in those days, but often didn't "finish the job," so there was a practice in those days of standing at the edge of a cliff or wall and strangling yourself so once you passed out you would plummet to your death. The whole process would legitimately be called "strangling himself" and could easily be (mis)translated into English as "hanging himself."
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Jas 3.1Nov 9 '13 at 17:58

3 Answers
3

I. Howard Marshall gives a concise statement of the options for harmonization in his commentary:

It is quite possible that Matthew or Luke is simply reporting what was commonly said in Jerusalem, and that we are not meant to harmonize the two accounts. If we do try to harmonzie (sic) them, the following possibilities arise: (1). Judas hanged himself (Matt.), but the rope broke and his body was ruptured by the fall (possibly after he was already dead and beginning to decompose); (2). What the priests bought with Judas’s money (Matt.) could be regarded as his purchase by their agency (Acts); (3). The field bought by the priests (Matt.) was the one where Judas died (Acts).

Marshall's three points address the first two differences you note (whether successfully or not depends I suppose on the reader).

As for the third difference about the origin of the names, it's possible for multiple stories to contribute to the giving of some name or sobriquet. For example, it's plausible that my nephew might be named both for me as well as for his great-grandfather who shares the same name. It would be equally valid to claim that he is named after his uncle as it would his great-grandfather.

Likewise, it seems plausible under Marshall's harmonization that the people of the day remembered the blood money and the bloody death of Judas both being connected with this field and so it became soon known as the Field of Blood. It would be perfectly valid were someone to ask how it got the name and be told that it was bought with blood money.

Points by @Soldarnal are persuasive. Please also consider that if Judas were an obese man at more than 200 lbs., and his "long drop" hanging were more than 5 feet, then he would have decapitated himself. His obese body, falling "headlong" (or top-down), would burst open upon hitting the ground. Please click here for an historical discussion of this eventuality in capital punishment.
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JosephMar 31 '13 at 1:41

Attempts to harmonise the two accounts should not use the salami technique of arguing. This means that all discrepancies should be addressed in the same argument, which must also be internally consistent. The important discrepancies are:

Judas through the money down in the Temple and the priests bought the field of blood; OR Judas, no doubt pleased by his sudden wealth, went himself and bought the field of blood (and was clearly not suicidal);

Judas committed suicide, OR Judas fell down and died (by misadventure?)

I propose that unless both discrepancies can be harmonised, then it is not satisfactory to attempt to harmonise just one. In that case, we must accept that at least one of the two accounts is fictional, and choose one - or acknowledge that we do not know how Judas died.

I also want to avoid suppositions or speculation, in favour of biblical hermeneutics. While it is vaguely possible that when Judas hanged himself he broke his neck, this is an unusual outcome; an even more improbable outcome would be that the consequent fall would result in his innards gushing out. In any case, why would each author report only half the story, and neither of them report that Judas' neck was broken?

My answer is that we do not know how Judas died - two different authors wrote what they thought would be the most satisfyingly disgusting death possible, one by suicide and the other in a revolting manner. The account in Acts 1:18, with Judas' bowels gushing out, brings to mind Acts 12:23, where Herod died a somewhat similar and equally a satisfyingly disgusting death.

I support this by pointing out that New Testament scholars have demonstrated that Luke's Gospel was substantially based on Mark's Gospel, which means that this author, who actually wrote anonymously, knew nothing about the life and mission of Jesus apart from what he learnt in Mark. The prologue of Luke's Gospel supports this, as he says that the gospel contains what he and his community most surely believe and that this came down to them from other sources that must once have included eyewitnesses. Now, if the author of Luke knew nothing about Jesus other than what he gleaned from Mark's Gospel, then he could not have known about the lonely death of a traitor. In the same way, Matthew's Gospel was substantially based on Mark's Gospel, containing some 90 per cent of the verses in Mark, and the very need for its anonymous author to carefully copy material from that source demonstrates he knew nothing about the life and mission of Jesus other than what was to be found in Mark. His death of Judas was a suicide, but (if true) a surely lonely suicide, not witnessed by anyone who could have passed on this information.

John Shelby Spong, author of Jesus for the Nonreligious, points out that Judas is a variant of Judah, and that in Genesis 37:26-27, it was Judah who sought money and received 20 pieces of silver; in Zechariah 11:14 the king was betrayed for 30 pieces of silver, which he hurled back into the temple just as Judas did in Matthew; in 2 Sam 15:12-17:23 Ahithophel hanged himself when his betrayal of King David was discovered,just as Judas did in Matthew. The 'field of blood', common to both accounts, also comes from the Old Testament.

(1). Judas hanged himself (Matt.), but the rope broke and his body was ruptured by the fall (possibly after he was already dead and beginning to decompose); (2). What the priests bought with Judas’s money (Matt.) could be regarded as his purchase by their agency (Acts); (3). The field bought by the priests (Matt.) was the one where Judas died (Acts).

-Marshall offering a possible reconciliaion. Which makes sense. This does not prove that Matthew and Luke had different understandings of the events surrounding Judas' death. However, it does prove that they do not necessarily contradict each other.